Prick tuna steaks all over with a fork and place in shallow glass dish.
Whisk oil, soy sauce, lemon juice, Dijon mustard, lemon peel, and garlic together in a bowl; pour over the tuna steaks. Cover dish with plastic wrap and refrigerate 1 to 3 hours.
Preheat grill for medium heat and lightly oil the grate.
Remove tuna from the marinade. Shake excess moisture from the steaks.
Pour the marinade into a small saucepan and bring to a boil. Reduce heat to medium-low and cook marinade at a simmer for 10 minutes.
Cook tuna on preheated grill, basting with boiled marinade, until cooked through, 5 to 6 minutes per side.
